In the Iranian nuclear deal, how can IAEA detect nuclear activity after 24 days? This is a question related to current events, but I want to ask about the physics, which are not explained in any news article that I can find.  
Ernest Moniz and John Kerry wrote an op-ed in the Washington Post about the recent nuclear deal with Iran. In it, they say that even though inspections can be delayed for 24 days, that delay is not a problem, because "environmental sampling can detect microscopic traces of nuclear activities even after attempts to remove evidence." 
My question is: how does this detection work, and how hard is it to defeat? I've studied some college level chemistry and physics, but I'm not an expert. My first guess was that the radioactive material in question would be emitting radiation that would alter the nuclei in the walls of any building or underground lab, and those altered nuclei would also be radioactive and detectable by the IAEA, even after 24 days.  Maybe I'm way off on that guess, but if that were true, I can imagine ways to create thick moveable walls (not easy, but within a government budget) that could hide activity and defeat a delayed inspection.  So, how does it work?
 A: 
Ernest Moniz and John Kerry wrote an op-ed in the Washington Post about the recent nuclear deal with Iran. In it, they say that even though inspections can be delayed for 24 days, that delay is not a problem .My question is: how does this detection work, and how hard is it to defeat? 

Let us have the info as to how the monitoring of Nuclear establishments/Nuclaer Weapon explosion/Power plant accidents get monitored through radiation fall out by Regulatory Authorities and then get a picture about the answer(probable) to the question:
Following Info. may be helpful-
The results of NRB-USA  monitoring have shown the presence of natural and
weapons fallout radiation and in a few instances, very low levels of radioactive material of nuclear plant origin.
A number of studies by the Radiation Public Health Project assert that levels of radioactive strontium-90 (Sr-90) are rising in the environment.
Strontium-90 (90Sr) is a radioactive isotope of strontium produced by nuclear fission, with a half-life of 28.8 years. 
It undergoes β− decay into yttrium-90, with a decay energy of 0.546 MeV. Strontium-90 has applications in medicine and industry and is an isotope of concern in fallout from nuclear weapons and nuclear accidents.
The biological half-life of strontium-90 in humans has variously been reported as from 14 to 600 days.
Sr-90 comes from three sources:
1. fallout from above-ground explosions of nuclear weapons testing 
2. radioactive releases from nuclear power plant accident and
3. radioactive releases from nuclear power plants into the environment.
By far, the largest source of Sr-90 in the environment (~99%) is from weapons testing fallout.
The  general focus on human health monitoring  here is on the isotopes cesium-137,  iodine-131, and strontium-90  since they are relatively volatile and thus can contaminate large areas. 
The concentration of Radio nuclides that may be released is limited to levels which, if inhaled or ingested continuously over the course of a year, would produce a dose of no more than 100 millirem. 
The limits are based on radiation protection recommendations of both the National Council on Radiation Protection Measurements and the International Commission on Radiological Protection organizations resulting from ongoing research.
Nuclear power plants are further limited by their license conditions to keep radioactive material in effluents “as low as reasonably achievable” so that dose criteria for releases to unrestricted areas are five millirem for releases into the air and three millirem for liquid releases.
All power plant operators are required to file a report of these discharges annually with the NRC. These reports, which are publicly
available.
The concentrations of radionuclides released into the environment from a nuclear facility are generally too low to be measurable outside the plant’s boundary. 
Ref:

http://www.geigercounter.org/radioactivity/isotopes.htm
https://en.wikipedia.org/wiki/Strontium-90
  www.nrc.gov › ... › Radiation Protection › How NRC Protects You

A: Once an air sample is taken, it is possible to analyze the constituent atomic species with high sensitivity using laser cooling in a magneto-optical trap. In particular, the amount of radioactive isotopes can be specified,
particularly well for Rubidium and Cesium.
I heard this on a conference. Maybe you can find more info if you search in the field of ultra-cold atoms or AMO physics.
